# The directed landscape

@article{Dauvergne2018TheDL, title={The directed landscape}, author={Duncan Dauvergne and Janosch Ortmann and B'alint Vir'ag}, journal={arXiv: Probability}, year={2018} }

The conjectured limit of last passage percolation is a scale-invariant, independent, stationary increment process with respect to metric composition. We prove this for Brownian last passage percolation. We construct the Airy sheet and characterize it in terms of the Airy line ensemble. We also show that last passage geodesics converge to random functions with Holder-$2/3^-$ continuous paths. This work completes the construction of the central object in the Kardar-Parisi-Zhang universality class…

## 80 Citations

Bulk properties of the Airy line ensemble

- Mathematics
- 2018

The Airy line ensemble is a central object in random matrix theory and last passage percolation defined by a determinantal formula. The goal of this paper to make it more accessible to probabilists.…

One-point distribution of the geodesic in directed last passage percolation

- MathematicsProbability Theory and Related Fields
- 2022

We consider the geodesic of the directed last passage percolation with iid exponential weights. We find the explicit one-point distribution of the geodesic location joint with the last passage times,…

Uniform convergence to the Airy line ensemble

- Mathematics
- 2019

We show that classical integrable models of last passage percolation and the related nonintersecting random walks converge uniformly on compact sets to the Airy line ensemble. Our core approach is to…

A PATCHWORK QUILT SEWN FROM BROWNIAN FABRIC: REGULARITY OF POLYMER WEIGHT PROFILES IN BROWNIAN LAST PASSAGE PERCOLATION

- MathematicsForum of Mathematics, Pi
- 2019

In last passage percolation models lying in the Kardar–Parisi–Zhang (KPZ) universality class, the energy of long energy-maximizing paths may be studied as a function of the paths’ pair of endpoint…

Exponents governing the rarity of disjoint polymers in Brownian last passage percolation

- MathematicsProceedings of the London Mathematical Society
- 2019

In last passage percolation models lying in the KPZ universality class, long maximizing paths have a typical deviation from the linear interpolation of their endpoints governed by the two‐thirds…

Coupling derivation of optimal-order central moment bounds in exponential last-passage percolation

- Mathematics, Computer Science
- 2022

New probabilistic arguments are introduced to derive optimal-order central moment bounds in planar directed last-passage percolation in i.i.d. exponential weights for both zero and near-stationary boundary conditions.

BULK PROPERTIES OF THE AIRY LINE ENSEMBLE BY DUNCAN DAUVERGNE

- Mathematics
- 2020

Abstract: The Airy line ensemble is a central object in random matrix theory and last passage percolation defined by a determinantal formula. The goal of this paper is to provide a set of tools which…

Non-existence of non-trivial bi-infinite geodesics in Geometric Last Passage Percolation

- Mathematics
- 2021

— We show non-existence of non-trivial bi-infinite geodesics in the solvable last-passage percolation model with i.i.d. geometric weights. This gives the first example of a model with discrete…

Point Fields of Last Passage Percolation and Coalescing Fractional Brownian Motions

- Mathematics, Physics
- 2021

We consider large-scale point fields which naturally appear in the context of the Kardar-ParisiZhang (KPZ) phenomenon. Such point fields are geometrical objects formed by points of mass…

Infinite geodesics, competition interfaces and the second class particle in the scaling limit

- Mathematics
- 2021

We establish fundamental properties of infinite geodesics and competition interfaces in the directed landscape. We construct infinite geodesics in the directed landscape, establish their uniqueness…

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Bulk properties of the Airy line ensemble

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- 2018

The Airy line ensemble is a central object in random matrix theory and last passage percolation defined by a determinantal formula. The goal of this paper to make it more accessible to probabilists.…

A PATCHWORK QUILT SEWN FROM BROWNIAN FABRIC: REGULARITY OF POLYMER WEIGHT PROFILES IN BROWNIAN LAST PASSAGE PERCOLATION

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In last passage percolation models lying in the Kardar–Parisi–Zhang (KPZ) universality class, the energy of long energy-maximizing paths may be studied as a function of the paths’ pair of endpoint…

Exponents governing the rarity of disjoint polymers in Brownian last passage percolation

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- 2019

In last passage percolation models lying in the KPZ universality class, long maximizing paths have a typical deviation from the linear interpolation of their endpoints governed by the two‐thirds…

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In last passage percolation models lying in the KPZ universality class, the energy of long energy-maximizing paths may be studied as a function of the paths' pair of endpoint locations. Scaled…

BULK PROPERTIES OF THE AIRY LINE ENSEMBLE BY DUNCAN DAUVERGNE

- Mathematics
- 2020

Abstract: The Airy line ensemble is a central object in random matrix theory and last passage percolation defined by a determinantal formula. The goal of this paper is to provide a set of tools which…